New Tweak to deal with Update module forgets data, says "No information is available about potential new releases..."

I'd like to offer a new tweak based on the issue at http://drupal.org/node/414950

It's always bugged me that this message appears, and now I see why it happens, and have found a fix to it which I commented about in the link above. Because checking for potential new releases can be intensive, Drupal itself doesn't do this by default, but I think now that many people would like to check each time they enable or disable modules rather than seeing this somewhat unsettling warning:

No information is available about potential new releases for currently installed modules and themes. To check for updates, you may need to run cron or you can check manually. Please note that checking for available updates can take a long time, so please be patient.

My questions are:
1. Do people (particularly the Drupal Tweaks maintainer) think this would be a nice tweak to include as a part of this module ?
2. If so, where would a checkbox to enable this Tweak best be located in the config for this module? I assume it should default to being off, right?

Of course if its easy for the maintainer to just go and add it where it makes sense, that'd be even better, I'm happy to stand down.